In recent years, 100 Gigabit-per-second (Gbps) long-distance optical transmission has been implemented by dual-polarization quadrature phase-shift keying (DP-QPSK) using a digital coherent technology. To further improve transmission capacity, greater-level modulation schemes such as 16 quadrature amplitude modulation (16-QAM), DP-16-QAM, or 64-QAM are being developed.
Multilevel modulation such as QPSK or DP-x-QAM (where x is 8, 16, 32, 64, . . . ) is performed using an I/Q optical modulator, where “I” is the in-phase component of the waveform and “Q” represents the quadrature component. Two Mach-Zehnder (abbreviated as “MZ”) interferometers are used for I/Q modulation. An optical modulator used of dual polarization such as DP-QPSK of DP-x-QAM has an I/Q optical modulator for each polarization component.
Using a I/Q optical modulator, a desired level of modulation is achieved by providing the following offsets between optical phases of lightwaves traveling through optical waveguides:                Shifting π radians between average optical phases of lightwaves travelling through two optical waveguides of the I-arm optical modulator;        Shifting π radians between average optical phases of lightwaves travelling through two optical waveguides of the Q-arm optical modulator; and        Shifting π/2 radians between average optical phases of lightwaves through the I-arm optical modulator and the Q-arm optical modulator.        
The average phase of lightwaves easily changes due to change in temperature or change over time. To maintain the above-noted phase differences in each of the I-arm and Q-arm, as well as between the I and Q arms, control operations are performed using a dither. See, for example, Patent Document 1 listed below. Dither is a pilot signal for control with sufficiently low frequency and small amplitude compared with the main signal.
Besides, in order to fix the operating point of an MZ optical modulator to a half-intensity point, a DC bias voltage is controlled by continuously applying dither pulses at a constant frequency fm onto the bias electrodes of the MZ optical modulator. See, for example, Patent Document 2 listed below.